Concise Fuzzy Representation of Big Graphs: a Dimensionality Reduction Approach

The enormous amount of data to be represented using large graphs exceeds in some cases the resources of a conventional computer. Edges in particular can take up a considerable amount of memory as compared to the number of nodes. However, rigorous edge storage might not always be essential to be able to draw the needed conclusions. A similar problem takes records with many variables and attempts to extract the most discernible features. It is said that the "dimension" of this data is reduced. Following an approach with the same objective in mind, we can map a graph representation to a k-dimensional space and answer queries of neighboring nodes by measuring Euclidean distances. The accuracy of our answers would decrease but would be compensated for by fuzzy logic which gives an idea about the likelihood of error. This method allows for reasonable representation in memory while maintaining a fair amount of useful information. Promising preliminary results are obtained and reported by testing the proposed approach on a number of Facebook graphs.